Perpetuity is a series of constant cash flows that continues indefinitely. The present value of a perpetuity can be calculated using the formula:
$$PV=\frac{C}{(1+r)^{1}}+\frac{C}{(1+r)^{2}}+\frac{C}{(1+r)^{3}}... \mmlToken{mo}[linebreak="auto"]{=}\frac{C}{r}$$
C— periodic payment;
r— discount rate.
Historically, perpetuities were British government bonds without a redemption date, known as consols (consolidated annuities). The UK government redeemed the last 2¾% and 2½% consols on July 5, 2015. Perpetuities are also commonly found in preference shares.
Growing Perpetuity
Growing perpetuity includes periodic growth unlike a regular perpetuity. The present value of a growing perpetuity can be calculated using the formula:
$$PV=C \times \left[ \frac{1}{(1+r)}+\frac{(1+g)}{(1+r)^{2}}+\frac{(1+g)^{2}}{(1+r)^{3}}...\right] \mmlToken{mo}[linebreak="auto"]{=}\frac{C}{r-g}$$
C— periodic payment;
g— growth rate;
r— discount rate.
See also:
Perpetuity FAQ
What is a perpetuity?
A perpetuity is a stream of equal cash flows that continues indefinitely.
What is the formula for the present value of a perpetuity?
The present value of a perpetuity is PV = C / r, where C is the periodic cash flow and r is the discount rate.
